On the order of accuracy for difference approximations of initial-boundary value problems

JOURNAL OF COMPUTATIONAL PHYSICS

卷:218

Article

Svard, Magnus ; Nordstrom, Jan

关键词: order of accuracy;    stability;    parabolic partial differential equations;    Navier-Stokes equations;    finite difference methods;    summation-by-parts;    boundary conditions;    boundary closure;   

DOI  :  10.1016/j.jcp.2006.02.014

来源: Elsevier

【 摘 要 】

Finite difference approximations of the second derivative in space appearing in, parabolic, incompletely parabolic systems of, and 2nd-order hyperbolic, partial differential equations are considered. If the solution is pointwise bounded, we prove that finite difference approximations of those classes of equations can be closed with two orders less accuracy at the boundary without reducing the global order of accuracy. This result is generalised to initial-boundary value problems with an mth-order principal part. Then, the boundary accuracy can be lowered m orders. Further, it is shown that schemes using summation-by-parts operators that approximate second derivatives are pointwise bounded. Linear and nonlinear computations, including the two-dimensional Navier-Stokes equations, corroborate the theoretical results. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free